needs some profit gain for continuous operation of proof-of-work

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The transaction fee collected from the block generation shall never be zero. Whatever technology we will have in the future, by the second law of thermodynamics, it is impossible to find a low probability event (here in bitcoin, to find a special hash) without consuming energy. As technology advances, mining rigs are approaching the theoretical energy consumption limit. These block generators will always need some Joule for their operation. Also, should the transaction fee be zero, these block generators would have no way to pay the energy bill after all 21M BTC are mined.

After all the 21M BTC are mined, the operation of these block generators is financed by selling the BTC they collect from the transaction fee. Suppose:

  1. the ultimate transaction fee per block is reaching F which can be estimated by the preference tendency for transaction fee.
  2. the ultimate BTC/Joule is reaching A
  3. the ultimate USD/Joule is reaching B
  4. the ultimate bitcoin network energy for one block is reaching C Joule
  5. the ultimate USD bitcoin economy ratio over the world bitcoin economy is reaching D
  6. the ultimate USD currency volume is reaching E
  7. the ultimate USD bitcoin economy ratio over the USD economy is reaching F

Then the ultimate BTC/Joule shall be C/F and ultimate BTC/USD exchange rate shall be C/F/B which is also EF/21000000/D .